Officers, officials, MPs and experts have all warned that trying to reconfigure the nation’s defences at the same time as seeking large cuts in the defence budget – and trying to complete the twin-track process in barely four months – is a recipe for strategic mistakes, financial misjudgements and political miscalculation.

Yet Dr Fox has publicly defended the SDSR process, backing both the basic need for cuts in spending and the way in which the Coalition is drawing up those cuts.

The revelation that he privately believes the process is “less and less defensible” and is indeed – as his critics have suggested – a reckless Treasury-led search for cuts will surely leave Dr Fox facing Labour accusations of hypocrisy.

But the greatest risk to Dr Fox lies in his dealings with his own Conservative colleagues, not least the Prime Minister.

The relationship between Dr Fox and Mr Cameron is beset by mutual suspicion and distrust.

The two men both fought for the Tory leadership in 2005. Mr Cameron may have won, but Dr Fox’s strong showing in the election established him as a heavyweight champion of the Conservative Right, a group that is none too fond of Mr Cameron.

Since taking office, Mr Cameron and Dr Fox have taken subtly different approaches to fundamental issues including the timetable for withdrawing British troops from Afghanistan.

And when Dr Fox summarily dismissed Sir Jock Stirrup, the Chief of the Defence Staff without informing No 10, the relationship deteriorated still further; Mr Cameron reasserted his authority by personally appointing Sir Jock’s successor.

And as the defence review has proceeded, the two men have differed again: Dr Fox is keen to cut thousands of men from the Army while defending the Royal Navy from deeper cuts; Mr Cameron is more cautious, and is siding with the Army.

Some of Mr Cameron’s allies regard Dr Fox with undisguised suspicion.

They have long thought that he plans to pick a fight with the Prime Minister over some emotive aspect of the defence budget and thus return to the backbenches to become the anointed leader of the Tory Right and await his chance to replace Mr Cameron.

Dr Fox’s friends dismiss that notion, insisting he is committed to government. But the Cameroons' doubts will only be fuelled by his letter, and by its publication.

A secondary risk for Dr Fox is that his letter will badly damage his already-fragile relationship with George Osborne, the Chancellor.

Mr Osborne has gone to great pains to stop spending ministers going over his head to the Prime Minister to plead their cause over budget cuts. His “star chamber” public expenditure committee of Cabinet ministers is supposed to be the final court of appeal on spending, not No 10.

Yet Dr Fox, as his letter makes clear, has deliberately excluded other NSC members -- who include Mr Osborne – from his appeal to Mr Cameron over the defence review.

Dr Fox and Mr Osborne have already publicly differed over the funding of the replacement for the Trident nuclear deterrent.

If Mr Osborne concludes that Dr Fox’s letter is a crude form of special pleading to lessen his budget cuts, the defence secretary will find his future dealings with the Treasury are even more awkward.